The video is trying to show a hypercube, which is an interesting idea. So...
A 3D cube's surface is six 2D squares. Each square is a plane in 3D space where one of the 3 co-ords is constant, each pair of faces has a different one of the 3 constant. If you drew only the X,Y and ignored the Z completely you'd draw 4 lines for the sides and two squares for the top and bottom, all overlaid. Knowing what a cube and square look like, is that understandable?
A 4D hypercube's surface is eight 3D cubes. You construct it from pairs of cubes in exactly the same way, each has either W,X,Y, or Z constant. So if you tried to draw that using only X,Y,Z you get two overlaid cubes and 6 square planes, each representing one of the faces of the hypercube.
With that in mind, does weird cube-in-cube make more sense?
As for reality? We have 3 spatial dimensions. Gases fill and expand in a 3d volume, gravity and EM propagate as the surface of a sphere giving inverse-distance-squared, the number of spatial dimensions is baked into physics.
A 3D cube's surface is six 2D squares. Each square is a plane in 3D space where one of the 3 co-ords is constant, each pair of faces has a different one of the 3 constant. If you drew only the X,Y and ignored the Z completely you'd draw 4 lines for the sides and two squares for the top and bottom, all overlaid. Knowing what a cube and square look like, is that understandable?
A 4D hypercube's surface is eight 3D cubes. You construct it from pairs of cubes in exactly the same way, each has either W,X,Y, or Z constant. So if you tried to draw that using only X,Y,Z you get two overlaid cubes and 6 square planes, each representing one of the faces of the hypercube.
With that in mind, does weird cube-in-cube make more sense?
As for reality? We have 3 spatial dimensions. Gases fill and expand in a 3d volume, gravity and EM propagate as the surface of a sphere giving inverse-distance-squared, the number of spatial dimensions is baked into physics.